Answer
$(-\infty,-\frac{5}{3}]\cup[\frac{1}{3},\infty)$
Work Step by Step
Step 1. Given $|3x+2|\geq3$, we have $3x+2\geq3$ or $3x+2\leq -3$
Step 2. The first inequality gives $3x\geq1$ which leads to $x\geq\frac{1}{3}$ or $[\frac{1}{3},\infty)$
Step 3. The second inequality gives $3x\leq-5$ which leads to $x\leq -\frac{5}{3}$ or $(-\infty,-\frac{5}{3}]$
Step 4. Use a number line to indicate the intervals as shown in the figure.
